自1980年代後期Hull & White、Wiggins、Johnson & Shanno等人相繼發表關於隨機波動度模型的文獻後，就有諸多的文獻對於在選擇權定價中考慮隨機波動度作更深入的分析與模型探討，然而關於隨機波動度的研究，在早期大多採用蒙地卡羅模擬法來分析選擇權的價格行為，但蒙地卡羅模擬法受限於運算效率不高與缺乏彈性，故在評價新奇選擇權，如美式選擇權、障礙選擇權時，並無法應用。故本文以Leisen（2000）的二元樹狀模型出發，探討在不同相關係數及參數設定下之各類選擇權的定價、避險參數及隱含波動度曲面模擬計算等主題。 最後我們得到下面幾點結論： 1.在收斂速度與運算效率方面，我們可以發現二元樹狀模型在分割期數n大於20時，計算價格與收斂價格的差距就非常微小，而若我們計算不同切割期數的最大價格差異也會發現其實都不到百分之一，因此整體而言，收斂速度是令人非常滿意的。 2.當期初波動度提高時，會縮小價外選擇權與B-S價格之間的價格誤差。當到期期限增加時，隱含波動度曲線會有整體提高的趨勢。 3.若提高波動係數σ為2.5時，則不論相關係數的正負情形，價內外的程度，皆會大幅提高選擇權的隱含波動度。而在相關係數為-0.5的時候，可以發現實證中常觀察到的隱含波動度微笑曲線，這可能代表著市場上的波動係數比我們預期中的都還來的高。 4.在進行不同相關係數及不同價內外程度下二元樹狀與單元樹狀模型的美式選擇權價格比較時，我們可以發現，若以二元樹狀模型為正確價格，當相關係數為負的時候，在價外的時候，單元樹狀模型有價格低估的現象，在價內的時候，則有價格高估的現象，而在相關係數為正的時候，則反之。 5.Leisen二元樹狀與封閉解的歐式向上出局賣權價格比較，在特定的參數設定之下，Leisen二元樹狀模型在評價歐式向上出局賣權的時候，當相關係數為負的時候，在價外的時候，模型價格會高於封閉解，在價內的時候，模型價格則會低於封閉解，而在相關係數為正的時候，則反之。

This doctoral thesis is comprised of four papers that all relate to the subject of Time Series Analysis. The first paper of the thesis considers point estimation in a nonnegative, hence non-Gaussian, AR(1) model. The parameter estimation is carried out using a type of extreme value estimators (EVEs). A novel estimation method based on the EVEs is presented. The theoretical analysis is complemented with Monte Carlo simulation results and the paper is concluded by an empirical example. The second paper extends the model of the first paper of the thesis and considers semiparametric, robust point estimation in a nonlinear nonnegative autoregression. The nonnegative AR(1) model of the first paper is extended in three important ways: First, we allow the errors to be serially correlated. Second, we allow for heteroskedasticity of unknown form. Third, we allow for a multi-variable mapping of previous observations. Once more, the EVEs used for parameter estimation are shown to be strongly consistent under very general conditions. The theoretical analysis is complemented with extensive Monte Carlo simulation studies that illustrate the asymptotic theory and indicate reasonable small sample properties of the proposed estimators. In the third paper we construct a simple nonnegative time series model for realized volatility, use the results of the second paper to estimate the proposed model on S&P 500 monthly realized volatilities, and then use the estimated model to make one-month-ahead forecasts. The out-of-sample performance of the proposed model is evaluated against a number of standard models. Various tests and accuracy measures are utilized to evaluate the forecast performances. It is found that forecasts from the nonnegative model perform exceptionally well under the mean absolute error and the mean absolute percentage error forecast accuracy measures. In the fourth and last paper of the thesis we construct a multivariate extension of the popular Diebold-Mariano test. Under the null hypothesis of equal predictive accuracy of three or more forecasting models, the proposed test statistic has an asymptotic Chi-squared distribution. To explore whether the behavior of the test in moderate-sized samples can be improved, we also provide a finite-sample correction. A small-scale Monte Carlo study indicates that the proposed test has reasonable size properties in large samples and that it benefits noticeably from the finite-sample correction, even in quite large samples. The paper is concluded by an empirical example that illustrates the practical use of the two tests.

This thesis is concerned with the small-time asymptotics and expansions of call option prices, when the log-return processes of the underlying stock prices follow several Levy-based models. To be specific, we derive the time-to-maturity asymptotic behavior for both at-the-money (ATM), out-of-the-money (OTM) and in-the-money (ITM) call-option prices under several jump-diffusion models and stochastic volatility models with Levy jumps. In the OTM and ITM cases, we consider a general stochastic volatility model with independent Levy jumps, while in the ATM case, we consider the pure-jump CGMY model with or without an independent Brownian component. An accurate modeling of the option market and asset prices requires a mixture of a continuous diffusive component and a jump component. In this thesis, we first model the log-return process of a risk asset with a jump diffusion model by combining a stochastic volatility model with an independent pure-jump Levy process. By assuming smoothness conditions on the Levy density away from the origin and a small-time large deviation principle on the stochastic volatility model, we derive the small-time expansions, of arbitrary polynomial order, in time-t, for the tail distribution of the log-return process, and for the call-option price which is not at-the-money. Moreover, our approach allows for a unified treatment of more general payoff functions. As a consequence of our tail expansions, the polynomial expansion in t of the transition density is also obtained under mild conditions. The asymptotic behavior of the ATM call-option prices is more complicated to obtain, and, in general, is given by fractional powers of t, which depends on different choices of the underlying log-return models. Here, we focus on the CGMY model, one of the most popular tempered stable models used in financial modeling. A novel second-order approximation for ATM option prices under the pure-jump CGMY Levy model is derived, and then extended to a model with an additional independent Brownian component. The third-order asymptotic behavior of the ATM option prices as well as the asymptotic behavior of the corresponding Black-Scholes implied volatilities are also addressed.

The dividend policy and the distribution of cash dividend can be of interest to the investors from many angles. Consequently, many theories have been built on the relevance of dividend policy and there are several theories proposing that dividends increase shareholder value. However, the most famous theory on dividend policy might be Miller and Modigliani's dividend irrelevance theory which implies that the dividend policy does not affect shareholder value. Although investors are concerned with shareholder value they are also concerned with achieving the highest possible return with the lowest volatility (risk). As many studies have focused on the dividend policy, especially dividend yield or the dividend payout ratio, and its relation with stock price movement we felt that there was a lack of information regarding the relation between return volatility and cash dividends. This resulted in the following research question: Does a change in cash dividend affect stock return volatility on NASDAQ OMX Stockholm? Answering this research question is the main purpose of the research. Additionally, the relationship between changes in cash dividend and return volatility will be compared in the different size segments that are to be found on NASDAQ OMX Stockholm. The study is quantitative with a deductive approach where historical data ranging from 2006-2012 has been gathered. Two measures of return volatility has been used, beta and standard deviation of return. Statistical tests have been conducted in an approach to answer the research question, mainly correlation tests and logistic regression analysis. No correlation between changes in cash dividend and changes in beta, nor changes in standard deviation were found. The same results were found when examining small, mid and large cap individually. In the logistic regression analysis no evidence was found that changes in dividend could explain changes in return volatility. Contrary to changes in dividend, the results indicate that the size of the company can explain changes in return volatility. Specifically, large cap companies explain increases in return volatility better than companies in the small cap segment. Therefore, the research question is concluded with no, a change in cash dividend does not affect stock return volatility. The findings could also be argued to be in support of the dividend irrelevance theory. Furthermore, the conclusion implies that investors need not regard the dividend policy when diversifying their portfolios. Additionally, managers need not be worried that a change in dividend policy should affect return volatility.

Η ακριβής πρόβλεψη της μελλοντικής μεταβλητότητας αποδεικνύεται ιδιαίτερα χρήσιμη για την τιμολόγηση παραγώγων προϊόντων και την αντιστάθμιση κινδύνων στη διαχείριση χαρτοφυλακίων. H τεκμαρτή μεταβλητότητα, όπως αυτή αντανακλάται στις τιμές των δικαιωμάτων προαίρεσης, αποτελεί την εκτίμηση της αγοράς για τη μελλοντική πραγματοποιηθείσα μεταβλητότητα και έχει αποδειχθεί ότι είναι πιο αποτελεσματική από την αντίστοιχη πρόβλεψη που προκύπτει από την ανάλυση ιστορικών χρονοσειρών. Η παρούσα διατριβή πραγματεύεται τη δημιουργία ενός δείκτη τεκμαρτής μεταβλητότητας για την Ελληνική χρηματιστηριακή αγορά, χρησιμοποιώντας έναν τρόπο υπολογισμού, ο οποίος είναι ανεξάρτητος από κάθε υπόδειγμα τιμολόγησης δικαιωμάτων προαίρεσης και βασίζεται σε ένα σταθμισμένο άθροισμα τιμών δικαιωμάτων. Η μεθοδολογία αυτή εφαρμόζεται για πρώτη φορά σε μια περιφερειακή, αναπτυσσόμενη αγορά, όπως το Χρηματιστήριο Αθηνών. Ο εν λόγω δείκτης τεκμαρτής μεταβλητότητας έχει τις προοπτικές να γίνει δείκτης αναφοράς των προσδοκιών για τη μελλοντική μεταβλητότητα στην Ελληνική μετοχική αγορά, καθώς αποδεικνύεται ότι υπερισχύει στατιστικά της ιστορικής μεταβλητότητας. Επίσης, οι επενδυτές του Χρηματιστηρίου Αθηνών μπορούν να χρησιμοποιούν το επίπεδό του και τις ημερήσιες μεταβολές του για να λάβουν επενδυτικές αποφάσεις, καθώς τα αποτελέσματα της οικονομετρικής ανάλυσης αποδεικνύουν ότι υπάρχει αρνητική και ασύμμετρη σχέση μεταξύ των μεταβολών του δείκτη τεκμαρτής μεταβλητότητας και των αποδόσεων του υποκείμενου μετοχικού δείκτη FTSE/Χ.Α.-20. Τέλος, η εμπειρική έρευνα καταγράφει την επιρροή της τεκμαρτής μεταβλητότητας των κυριοτέρων χρηματιστηρίων του εξωτερικού στην εγχώρια τεκμαρτή μεταβλητότητα, ενώ επιπλέον προσπαθεί να αναπτύξει ένα υπόδειγμα για την πρόβλεψη της τεκμαρτής μεταβλητότητας αυτής καθαυτής. / In this thesis a new measure of Greek stock market volatility based on the implied volatility of FTSE/ATHEX-20 index options is proposed. Greek Implied Volatility Index is calculated using the model-free methodology that involves option prices summations and is independent from the Black and Scholes pricing formula. The specific method is applied for the first time in a peripheral and illiquid market as the Athens Exchange. The empirical findings suggest that implied volatility includes information about future volatility beyond that contained in past realized volatility and in addition, prove that there is a statistically significant negative and asymmetric contemporaneous relationship between implied volatility changes and the underlying equity index returns. Finally, the volatility transmission effects on the Greek stock exchange from the major global exchanges are tested and documented. The basis of the international integration analysis, instead of the commonly used realized returns or variances, is the implied volatilities, as proxied by the corresponding implied volatility indices.

Some recent works in the field of mathematical finance have brought new light on the importance of studying the regularity and the tail asymptotics of distributions for certain classes of diffusions with non-globally smooth coefficients. In this Ph.D. dissertation we deal with some issues in this framework. In a first part, we study the existence, smoothness and space asymptotics of densities for the solutions of stochastic differential equations assuming only local conditions on the coefficients of the equation. Our analysis is based on Malliavin calculus tools and on " tube estimates " for Ito processes, namely estimates for the probability that the trajectory of an Ito process remains close to a deterministic curve. We obtain significant estimates of densities and distribution functions in general classes of option pricing models, including generalisations of CIR and CEV processes and Local-Stochastic Volatility models. In the latter case, the estimates we derive have an impact on the moment explosion of the underlying price and, consequently, on the large-strike behaviour of the implied volatility. Parametric implied volatility modeling, in its turn, makes the object of the second part. In particular, we focus on J. Gatheral's SVI model, first proposing an effective quasi-explicit calibration procedure and displaying its performances on market data. Then, we analyse the capability of SVI to generate efficient approximations of symmetric smiles, building an explicit time-dependent parameterization. We provide and test the numerical application to the Heston model (without and with displacement), for which we generate semi-closed expressions of the smile

This thesis adopts an empirical approach to examine various market microstructure issues, using data from the National Stock Exchange of India (NSE). Whilst the respective empirical analyses may be considered as self-contained investigations, they are primarily linked through the common objective of understanding the mechanics of the pricing process as it occurs on actual markets, using the NSE as exemplar. The first major focus of the dissertation is non-synchronous trading: empirical evidence of nonsynchronicity is obtained by testing for predictability as between indices of different levels of liquidity. A simple test of the analysis of trading-break returns is proposed to infer whether predictability may be mainly attributable to non-synchronous trading or whether it constitutes a delayed adjustment of traders' expectations. The second question tackled in the thesis is whether volatility on the NSE may be considered as justified or excessive. Rathert han adopting the established methodology of comparing stock price changes to information about expected dividends, the research question is split up into two subsidiary ones. The first question is whether volatility is related to information flows, whilst the second related questionc oncernst he relationship betweenv olatility and returns. Three sources of excessive volatility are pin-pointed. Monday effects are found in index data but not in the underlying stocks-indicating index fluctuations which are not information-related. A second indicator of excessive price movements is the pronounced volatility which coincides with the fiscal year end of quoted companies but which is not accompanied by a similar increase in long-term returns. A third indication of unjustified price fluctuations is that volatility seems unrelated to returns when considering a long-term time series. The third topic of the thesis relates to the efficacy of opening and closing call auctions. This issue may be considered as the crux of the dissertation and it is tackled by analysing the effects of the suspension of a call auction system on NSE. Changes in volatility, efficiency and liquidity following the suspension are analysed, and an event study is presented. The relationship between call auctions and long-term volatility is also investigated. The findings suggest that the expected benefits of call auctions may not always materialise, possibly due to an inappropriately structured auction, or because a liquidity threshold for stocks must be surpassed for the expected benefits to accrue.

Submitted by Cristina Tessari (tinatessari@gmail.com) on 2016-06-09T13:51:42Z No. of bitstreams: 1 DissertationEPGE_CristinaTessari2016.pdf: 1264081 bytes, checksum: 14e65157457bfe8deea5353bb192a0af (MD5) / Approved for entry into archive by Marcia Bacha (marcia.bacha@fgv.br) on 2016-06-29T14:03:25Z (GMT) No. of bitstreams: 1 DissertationEPGE_CristinaTessari2016.pdf: 1264081 bytes, checksum: 14e65157457bfe8deea5353bb192a0af (MD5) / Approved for entry into archive by Marcia Bacha (marcia.bacha@fgv.br) on 2016-06-29T14:06:59Z (GMT) No. of bitstreams: 1 DissertationEPGE_CristinaTessari2016.pdf: 1264081 bytes, checksum: 14e65157457bfe8deea5353bb192a0af (MD5) / Made available in DSpace on 2016-06-29T14:07:23Z (GMT). No. of bitstreams: 1 DissertationEPGE_CristinaTessari2016.pdf: 1264081 bytes, checksum: 14e65157457bfe8deea5353bb192a0af (MD5) Previous issue date: 2016-03-22 / We use Brazilian data to compute monthly idiosyncratic moments (expected skewness, realized skewness, and realized volatility) for equity returns and assess whether they are informative for the cross-section of future stock returns. Since there is evidence that lagged skewness alone does not adequately forecast skewness, we estimate a cross-sectional model of expected skewness that uses additional predictive variables. Then, we sort stocks each month according to their idiosyncratic moments, forming quintile portfolios. We find a negative relationship between higher idiosyncratic moments and next-month stock returns. The trading strategy that sells stocks in the top quintile of expected skewness and buys stocks in the bottom quintile generates a significant monthly return of about 120 basis points. Our results are robust across sample periods, portfolio weightings, and to Fama and French (1993)’s risk adjustment factors. Finally, we identify a return reversal of stocks with high idiosyncratic skewness. Specifically, stocks with high idiosyncratic skewness have high contemporaneous returns. That tends to reverse, resulting in negative abnormal returns in the following month. / In the first chapter, we test some stochastic volatility models using options on the S&P 500 index. First, we demonstrate the presence of a short time-scale, on the order of days, and a long time-scale, on the order of months, in the S&P 500 volatility process using the empirical structure function, or variogram. This result is consistent with findings of previous studies. The main contribution of our paper is to estimate the two time-scales in the volatility process simultaneously by using nonlinear weighted least-squares technique. To test the statistical significance of the rates of mean-reversion, we bootstrap pairs of residuals using the circular block bootstrap of Politis and Romano (1992). We choose the block-length according to the automatic procedure of Politis and White (2004). After that, we calculate a first-order correction to the Black-Scholes prices using three different first-order corrections: (i) a fast time scale correction; (ii) a slow time scale correction; and (iii) a multiscale (fast and slow) correction. To test the ability of our model to price options, we simulate options prices using five different specifications for the rates or mean-reversion. We did not find any evidence that these asymptotic models perform better, in terms of RMSE, than the Black-Scholes model. In the second chapter, we use Brazilian data to compute monthly idiosyncratic moments (expected skewness, realized skewness, and realized volatility) for equity returns and assess whether they are informative for the cross-section of future stock returns. Since there is evidence that lagged skewness alone does not adequately forecast skewness, we estimate a cross-sectional model of expected skewness that uses additional predictive variables. Then, we sort stocks each month according to their idiosyncratic moments, forming quintile portfolios. We find a negative relationship between higher idiosyncratic moments and next-month stock returns. The trading strategy that sells stocks in the top quintile of expected skewness and buys stocks in the bottom quintile generates a significant monthly return of about 120 basis points. Our results are robust across sample periods, portfolio weightings, and to Fama and French (1993)’s risk adjustment factors. Finally, we identify a return reversal of stocks with high idiosyncratic skewness. Specifically, stocks with high idiosyncratic skewness have high contemporaneous returns. That tends to reverse, resulting in negative abnormal returns in the following month.

Att kunna gör en effektiv undersökning av det flyktiga minnet är något som blir viktigare ochviktigare i IT-forensiska utredningar. Dels under Linux och Windows baserade PC installationermen också för mobila enheter i form av Android och enheter baserade andra mobila opperativsy-stem.Android använder sig av en modifierad Linux-kärna var modifikationer är för att anpassa kärnantill de speciella krav som gäller för ett mobilt operativsystem. Dessa modifikationer innefattardels meddelandehantering mellan processer men även ändringar till hur internminnet hanteras ochövervakas.Då dessa två kärnor är så pass nära besläktade kan samma grundläggande principer användas föratt dumpa och undersöka minne. Dumpningen sker via en kärn-modul vilket i den här rapportenutgörs av en programvara vid namn LiME vilken kan hantera bägge kärnorna.Analys av minnet kräver att verktygen som används har en förståelse för minneslayouten i fråga.Beroende på vilken metod verktyget använder så kan det även behövas information om olika sym-boler. Verktyget som används i det här examensarbetet heter Volatility och klarar på papperet avatt extrahera all den information som behövs för att kunna göra en korrekt undersökning.Arbetet avsåg att vidareutveckla existerande metoder för analys av det flyktiga minnet på Linux-baserade maskiner (PC) och inbyggda system(Android). Problem uppstod då undersökning avflyktigt minne på Android och satta mål kunde inte uppnås fullt ut. Det visade sig att minnesanalysriktat emot PC-plattformen är både enklare och smidigare än vad det är mot Android. / The ability to be able to make a efficient investigation of volatile memory is something that getsmore and more important in IT forensic investigations. Partially for Linux and Windows based PCsystems but also for mobile devices in the form of the Android or devices based on other mobileoperative systems.Android uses a modified Linux kernel where the modifications exclusively are to adapt it to thedemands that exists in a operative system targeting mobile devices. These modifications containsmessage passing systems between processes as well as changes to the memory subsystems in theaspect of handling and monitoring.Since these two kernels are so closely related it is possible to use the same basic principles for dum-ping and analysing of the memory. The actual memory dumping is done by a kernel module whichin this report is done by the software called LiME which handles both kernels very well.Tools used to analyse the memory needs to understand the memory layout used on the systemin question, depending on the type of analyse method used it might also need information aboutthe different symbols involved. The tool used in this project is called Volatility which in theory iscapable of extracting all the information needed in order to make a correct investigation.The purpose was to expand on existing methods for analysing volatile memory on Linux-basedsystems, in the form of PC machines as well as embedded systems like Android. Difficulties arisedwhen the analysing of volatile memory for Android could not be completed according to existinggoals. The final result came to show that memory analysis targeting the PC platform is bothsimpler and more straight forward then what it is if Android is involved.

In this thesis, we derive a closed-form approximation to the implied volatility for a European option, assuming that the underlying asset follows the generalized Heston model. A new para- meter is added to the Heston model which constructed the generalized Heston model. Based on the results in Lorig, Pagliarani and Pascucci [11], we obtain implied volatility expansions up to third-order. We conduct numerical studies to check the accuracy of our expansions. More specifically we compare the implied volatilities computed using our expansions to the results by Monte Carlo simulation method. Our numerical results show that the third-order implied volatility expansion provides a very good approximation to the true value.